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Automatic differentiability and characterization of cocycles of holomorphic flows

Authors: Farhad Jafari, Thomas Tonev and Elena Toneva
Journal: Proc. Amer. Math. Soc. 133 (2005), 3389-3394
MSC (2000): Primary 47D03; Secondary 47B38
Published electronically: June 7, 2005
MathSciNet review: 2161164
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Abstract: In this paper we prove that cocycles of holomorphic flows on domains in the complex plane are automatically differentiable with respect to the flow parameter, and their derivatives are holomorphic functions. We use this result to show that, on simply connected domains, an additive cocycle is a coboundary if and only if this cocycle vanishes at the fixed point of the flow.

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Farhad Jafari
Affiliation: Department of Mathematics, University of Wyoming, Laramie, Wyoming 82071-3036

Thomas Tonev
Affiliation: Department of Mathematical Sciences, University of Montana, Missoula, Montana 59812-1032

Elena Toneva
Affiliation: Department of Mathematics, 216 Kingston Hall, Eastern Washington University, Cheney, Washington 99004-2418

Keywords: Flow, cocycle, infinitesimal generator
Received by editor(s): March 7, 2003
Received by editor(s) in revised form: July 1, 2004
Published electronically: June 7, 2005
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2005 American Mathematical Society

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